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abstract

The problem of finding appropriate weights for combining several density forecasts is an important issue that is currently being debated in the forecast combination literature. A recent paper by Hall and Mitchell (2007) proposes that density forecasts be combined using the weights obtained from solving an optimization problem. This paper documents the properties of this optimization problem through a series of simulation experiments. When the number of forecasting periods is relatively small, the optimization problem often produces solutions that are dominated by a number of simple alternatives. Crown Copyright © 2015 Published by Elsevier B.V. on behalf of International Institute of Forecasters. All rights reserved.

4. Concluding comments

The idea of using a training sample for parameter estimation before forecasting out-of-sample is acknowledged widely in the forecasting literature. The simulation and empirical results considered in this paper indicate the necessity of using a training sample for the optimal weights of Hall and Mitchell (2007) when combining forecasts. If no such training sample is used, one risks ending up with a corner solution. This is an artefact of the optimization problem given by Eq. (6) when the number of forecasting periods, T , is small. When T is sufficiently large, the asymptotic theory used by Hall and Mitchell (2007) and Geweke and Amisano (2011) to justify the optimal weights is valid, and the optimal weights have the expected properties. If one wishes the weights to behave as would be expected from theory, the authors’ practical recommendation is to use at least 36 data points (three years of monthly data) when solving the optimization problem. Alternatively, one can use the weights proposed by Pauwels and Vasnev (2012), which do not need this extensive training period.